1 Basic Drabability [s Pointa] Bayea' |lule: Consider a mealcal diagnoin prablem in which a randam wariable C can take two values Le. 1 indicating that the patient hin at particular form of cancer and 1 indlating that the patient does not have cancer. A farnous labaratary performs an expenaive diagnasic test T to desect of a particular patient is positive or negatie. Therelore the viruble T in also a rindom variable that takes the walues +1 ar 1. We have prior knowledge that over the intire populatian af pesple only cobs hwoe this divease. furthermore, the lab test is only an imperfect indicasar of the dasase. The teit returm a correct poo tive revelt in gass di the caies in which the which the disease in nat prient. In other cinin, the sest returns the apposise reule. The above utuation can be summariad by the fallowirg prabuaticia P[C=1]=a.oct p[C=1]=a.25d, P[T=+1C=1]=0.58 and P[T=1C=1)=0.02 P[T=1C=1]=0.00 and P[T=1C=1]=0.97 Cheen that a new putiont hin been tested ponative i.e. T=1, use Dayes' rule to compule the probabilities PC=1T=1 and D(C=1T=1). 1 2 Multiple Randem Variabies [3+4+2] The joint demify of twa rindom variables x and Y h given in f(x,y)=C(x+2y)if0